Lower bounds on the variance of deterministic signal parameter estimators using Bayesian inference

Bayesian estimators have been applied for both random and deterministic parameters. In the Bayesian estimation of deterministic parameters, the randomness is introduced only through the observations, and the prior distributions are adopted to impose certain constraints. In such cases, neither the well known Cramer-Rao lower bound (CRLB) or the posterior CRLB can be used reasonably as the performance lower bounds. We extend the theory of CRLB under the Bayesian framework to provide the lower bounds for both unbiased and biased Bayesian estimators of deterministic parameters. An example is provided to show the effectiveness of the proposed lower bound over other popular lower bounds.